1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mezya [45]
3 years ago
8

The volume of a sphere is increasing at a constant rate of 141 cubic feet per minute. At the instant when the radius of the sphe

re is 11 feet, what is the rate of change of the radius? The volume of a sphere can be found with the equation V=4/3pi r^3 . Round your answer to three decimal places.
Mathematics
1 answer:
ch4aika [34]3 years ago
6 0

Answer:

0.093 ft/min

Step-by-step explanation:

V = 4/3 π r³

Take derivative with respect to time:

dV/dt = 4π r² dr/dt

Plug in values:

141 = 4π (11)² dr/dt

dr/dt = 141 / (484π)

dr/dt ≈ 0.093

The radius is increasing at 0.093 ft/min.

You might be interested in
Evaluate Cot0 if sin0= square root of 6/5
Lina20 [59]
To evaluate cot θ given that sinθ=√6/5 we shall have:
sin θ=opposite/hypotenuse
hence
opposite=√6
hypotenuse=5
thus the adjacent will be found using the Pythagorean theorem
c²=a²+b²
plugging in the value we get:
5²=(√6)²+b²
b²=25-6
b²=19
b=√19
thus
adjacent=√19
but
cotθ=1/tanθ
tanθ=√6/√19
hence:
cotθ=√19/√6
6 0
2 years ago
Please answer this and simplify
777dan777 [17]

Answer:

volume = x(x+2)(2x+1) = 2x^3+5x^2+2x

a = 2

b = 3

c = 5

d = 2

e = 2

f = 1

6 0
2 years ago
Read 2 more answers
Miriam has a bamboo plant that is 23 centimeters tall the plant grows at a rate of 2 centimeters a week which recursive formula
galben [10]
Ok so... W is week. It would be 20+2w. Because we start with the plants hight (20) and them it grows two cm per week, so 2w.
5 0
3 years ago
Plz help with this word problem
s344n2d4d5 [400]
Well, this problem is best solved by setting up a system of two linear equations.

A linear equation can be defined 
y=mx+b
where 
b=initial value (when x=0), and
m=rate of increase or decrease.

In the given example, the x-axis represents hour, and the y-axis, number of cells.

Chemical #1 
initial value = b = 12000 cells
rate = m = -4000 / hr
The equation is therefore 
y1=-4000x+12000......................(1)

Similarly, for chemical #2
initial value = b = 6000 cells
rate = m = -3000 / hr
The equation is therefore
y2=-3000x+6000 .......................(2)

The time the two will have an equal sized colony would represent the solution of the system of equations (1) and (2), i.e. when  y1=y2
which means
-4000x+12000 = -3000x+6000
transpose and solve for x
4000x-3000x = 12000-6000
1000x=6000
x=6 hours.

At 6 hours from the start, 
y=-4000x+12000 = -4000*6+12000 = -24000+12000 = -12000 cells

So the solution is x=6, y=-12000, or (6,-12000)

Physical interpretation
Since cells cannot have a negative number, the two are actually equal before six hours, when they are both zero.
Case 1: y=0 when x=3
Case 2: y=0 when x=2

Therefore, after three hours, both trials will have zero cells.

You have to judge whether to give the mathematical solution (x=6,y=-12000) or the physical interpretation (x=3, y=0) as the answer.


6 0
3 years ago
Read 2 more answers
HELLLLLLLLLLLLLLLLLPPPPPPPPP
ahrayia [7]

Answer:

C

Step-by-step explanation:

-6(-2/3 + 2x)

~Distribute

4 - 12x

Best of Luck!

3 0
3 years ago
Read 2 more answers
Other questions:
  • Help plz answer this
    7·2 answers
  • 182,886 rounded to the nearest tenth
    7·2 answers
  • I WILL GIVE 40 POINTS FOR EACH QUESTION REALLY NEED HELP THERE ANOTHER POST FOR THE OTHER QUESTION IT WILL BE ANOTHER 40 AS WELL
    12·2 answers
  • Find m2ABC<br> (3x + 8)<br><br> (5x - 40)
    9·1 answer
  • Julia bought name tags for a party. Each name tag is 334 inches wide and 213 inches high. The formula for the area of a rectangl
    5·1 answer
  • 8 g(x)=−3x−8g, left parenthesis, x, right parenthesis, equals, minus, 3, x, minus, 8 g ( g(g, left parenthesis ) = 10 )=10right
    12·2 answers
  • Write an equation that represents the graph
    5·1 answer
  • To train for a race, Scott's want to run 20 miles this week . he runs 1/4 of the miles on Monday. If he runs 2 miles on Tuesday
    12·1 answer
  • How is 0.623 expressed as a percentage?
    14·2 answers
  • How is the product of 2 and –5 shown using integer tiles? 2 positive tiles and 5 negative tiles. 2 negative tiles and 5 positive
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!